Operator Lowering †

Abstract

Abstract In the history of Western linguistic analysis there are two distinct but not totally unrelated traditions, the grammatical tradition and the logical tradition. In the grammatical tradition, which originated in classical antiquity as an application for practical (normative) purposes of the existing standard system of logical analysis, quantifiers never occupied a special place: they were not recognized as a separate category. But in the logical tradition they were. In the Aristotelian system of predicate calculus (APC) the general distinction between subject and predicate was applied, and, as we shall see presently, a calculus was developed that took into account only quantified subjects, not other nominal constituents under a quantifier. Traditional grammar owes its parsing method mainly to this Aristotelian tradition of the subject-predicate distinction, but since grammar was (and remained for a long time) an applied and normative discipline, not at all concerned with the logical calculus of entailments, no need was felt to distinguish quantified subjects as a separate category. Quantified NPs were considered to have the same structure as non-quantified NPs, and quantifying determiners were not taken to differ in any essential way from definite determiners such as the definite article or demonstrative or possessive pronouns.